The early colonists were not exclusively British so one would be ignoring history to suppose it. For example southern states were and are ethnicaly Hispanic. Then we have French influences to take into account.
The Hillbilly theory is flatout false. That term is recent, used be more like Mountainmen etc. IOW These people knew very little about the significance of King Billy and they would more likely been preaching about the Bill of Rights. Please do be aware - it might save your life if you ever travel the back woods - that not all mountain people are descended or related to British descended folks - They could have anglo names but that could be where you discover a costly fact of life in the American melting pot. Schlobsmalsoazioedee was simplified as Smith.
Bluegrass - the color of the grass - is associated with the State of Kentucky. The music itself is a product of Banjo Picking styles evolving not some genius discovery by Bill Munroe. He may have labelled it - Bluegrass - but he most certainly did not invent it! See Earl Scruggs Fiddler and Banjoist.
To gain some insight into this one needs to study instrument constuction, string technology and playeing technique of that period. Modern instruments use steel strings while the older used gut. Modern use steel picks in the uppicking style the old one was downpicking with no picks attached.
The modern tunes show the influence of the earlier lutish style - the tunes follow a 'modal' pattern - listen to Old Timey Fiddle and Banjo recordings - but also evolved newer tunes as well.
Since US folk flowed from fiddling styles applied to both native melodies - OT - and adopted French/British/Spanish etc there is no way that one can exclusively account for BG as an evolution of British Folk in the new world.
American folk Dance music does take lots of strains from the old countries but they include lots of things that are not celtic. For example I have not included Native American singing but it too has an enormous impact.
One must also be aware that American Fiddling is very close to classical violin in bowings and style, often chosen from classicaly training. This is as true today as it was 100 years ago, fiddlers in the US tend to be classicaly trained vioinists.
So the music is far far simpler in content and more disciplined than celtic. Bowing tends to be mostly down for significant beats, like Scottish Fiddling but not Scottish tunes. In fact what often happens - see Breakdowns - a player finds a bowing that is very rhythmic and develops that. IOW American Fiddle begins with rhythm - most often seen in the everpresent banjo or more recently guitar backing - not melody. As a result one can find thousands of variations on a simple strain.
Other names associated with the BG tradition - the Stanley Bros - Jesse Mc Reynolds - Scruggs and Flatt.
For a long time these folks distanced themselves from the so called Bluegrass craze, in fact even Bill the Mandoline player of the revolution - would lament what the followers of the craze were doing.
Finaly and to me very interesting trends - today one will see about as many high end Old Timey open back Banjos and Tenors being bought as the Resonator type. We are in a time of evolution again, and like the old Bob Diddle song says ' the times are a changin '.
Bluegrass is going the same road as OT Banjo and Fiddle music, todays kids are playing celtic out of boredom with what they inherited just as the BG revolution did in its day. In short the BG craze nearly obliterated the OT Banjo - now celtic is doing the same to BG.